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Sorting Algorithms Algorithm Analysis and Big-O Searching Checkout - - PowerPoint PPT Presentation
Sorting Algorithms Algorithm Analysis and Big-O Searching Checkout - - PowerPoint PPT Presentation
Sorting Algorithms Algorithm Analysis and Big-O Searching Checkout SortingAndSearching project from SVN Exam results Lets see Shlemiel the Painter Be able to describe basic sorting algorithms: Selection sort Insertion sort
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Let’s see…
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Shlemiel the Painter
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Be able to describe basic sorting algorithms:
- Selection sort
- Insertion sort
- Merge sort
- Quicksort
Know the run-time efficiency of each Know the best and worst case inputs for each
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Basic idea:
- Think of the list as having a sorted part (at the
beginning) and an unsorted part (the rest)
- Find the smallest number
in the unsorted part
- Move it to the end of the
sorted part (making the sorted part bigger and the unsorted part smaller)
Repeat until unsorted part is empty
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Profiling: collecting data on the run-time
behavior of an algorithm
How long does selection sort take on:
- 10,000 elements?
- 20,000 elements?
- …
- 80,000 elements?
Q1
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Analyzing: calculating the performance of an
algorithm by studying how it works, typically mathematically
Typically we want the relative performance as
a function of input size
Example: For an array of length n, how many
times does selectionSort() call compareTo()?
Handy Fact
Q2-7
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In analysis of algorithms we care about
differences between algorithms on very large inputs
We say, “selection sort takes on the order of
n2 steps”
Big-Oh gives a formal definition for
“on the order of”
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We write f(n) = O(g(n)), and
say “f is big-Oh of g”
if there exists positive constants c and n0 such that 0 ≤ f(n) ≤ c g(n)
for all n > n0
g is a ceiling on f
Q8,9
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Perhaps it’s time for a break.
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Basic idea:
- Think of the list as having a sorted part (at the
beginning) and an unsorted part (the rest)
- Get the first number in the
unsorted part
- Insert it into the correct
location in the sorted part, moving larger values up to make room
Repeat until unsorted part is empty
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Profile insertion sort Analyze insertion sort assuming the inner
while loop runs that maximum number of times
What input causes the worst case behavior?
The best case?
Does the input affect selection sort?
Q10-19 Ask for help if you’re stuck!
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Consider:
- Find the CRN of CSSE220 in the printed schedule
- Find the course whose CRN is 2331
Why is one task harder than the other? For searching unsorted data, what’s the worst
case number of comparisons we would have to make?
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A divide and conquer strategy Basic idea:
- Divide the list in half
- Decide whether result should be in upper or lower
half
- Recursively search that half
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What’s the best case? What’s the worst case? We use recurrence relations to analyze
recursive algorithms:
- Let T(n) count the number of comparisons to search
an array of size n
- Examine code to find recursive formula of T(n)
- Solve for n
Q20-21
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